Question

solve and check the linear equation.
$16 - \frac{x}{3} = \frac{x}{5}$
what is the solution? select the correct choice below and, if necessary, fill in the answer box to complete your choice
a. the solution set is { }
b. the solution set is {x | x is a real number}.
c. the solution set is $\varnothing$.

Explanation:

Step1: Eliminate denominators

Multiply all terms by 15 (LCM of 3 and 5):
$$15\times16 - 15\times\frac{x}{3} = 15\times\frac{x}{5}$$
$$240 - 5x = 3x$$

Step2: Isolate x terms

Add $5x$ to both sides:
$$240 = 3x + 5x$$
$$240 = 8x$$

Step3: Solve for x

Divide by 8:
$$x = \frac{240}{8} = 30$$

Step4: Verify the solution

Substitute $x=30$ into original equation:
Left side: $16 - \frac{30}{3} = 16 - 10 = 6$
Right side: $\frac{30}{5} = 6$
Both sides are equal, so $x=30$ is valid.

Answer:

A. The solution set is {30}